Abstract
We construct a compact, convex ancient solution of mean curvature flow in $\mathbb{R}^{n+1}$ with $O(1) \times O(n)$ symmetry that lies in a slab of width $\pi$. We provide detailed asymptotics for this solution and show that, up to rigid motions, it is the only compact, convex, $O(n)$-invariant ancient solution that lies in a slab of width $\pi$ and in no smaller slab.
Funding Statement
The second author was partially supported by an
Alexander von Humboldt fellowship.
The third author was partially supported by EPSRC
grant no. EP/M024512/1.
Citation
Theodora Bourni. Mat Langford. Giuseppe Tinaglia. "Collapsing ancient solutions of mean curvature flow." J. Differential Geom. 119 (2) 187 - 219, October 2021. https://doi.org/10.4310/jdg/1632506300
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